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prove that root 3 is irrational number?
Suppose assume root3 is a rational number.Thenroot(3) can be expressed as: = p/qwhere p,q are the integers.then write,p =qroot3squaring both sides,p^2 = 3q^2 Now for any integer (p,q)the eqn. is not going to satify.Therfore from the contradiction it gets untrue.Hence it is not a rational number then therfore, it is a irrational number.
prove that for all p,q that equation not satisfies.and send post the answer . need proof for that,how do I conclude that is not going to satisfy by directly telling so just post it
WE NEED TO PROVE THAT FOR ALL P,Q SUCH THAT P2=3Q2 DOESN’T EXIST WHERE P,Q BELONGS TO Z. so justify ur answer with proper reason ….
P and Q are natural numbers, and hence in the prime factorization of P2 and Q2, every prime factor appears to an even power. Now in the equation P2=3Q2 we have a contradiction as LHS has an even exponent for 3, whereas on RHS exponent of 3 is odd. So no such pair (P,Q) exists. Hence is irrational
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